Introduction

to-do: add intro

Methods

The data is comprised of monthly payment performance and, where available, demographic data for residents. 32,385 monthly observations over 813 homes, 812 accounts and 621 users were initially observed. To avoid data quality issues and to analyze any potential churn and default trends, for Frog Hollow households the analysis will drop values in October 2021 until April 2022. This narrowed dataset is comprised of 31,704 observations; the homes, accounts and users did not change.

The first ten rows of the data are presented, grouped by account number. Unique identifiers were replaced with sequential IDs.

• Tenure: length in months each account was active
• Payment_Method: either card or ACH/direct debit method
• temp_solar: annual (right?) solar allocation in kWh
• Churn: binary _var_iable capturing if an account left the solar farm
• defauted: binary variable capturing if account holder defaulted on payment
• Income: Low (<$50,000) or High (>$50,000)
• Solar_Farm: Either Howell or Frog Hollow

Descriptive Statistics

temp <- raw %>%
 group_by(user_id,utility_acct_number) %>%
  summarise(tenure = length(unique(date_concat)),
            count_accts = n(),
            default = sum(default_tag=="Defaulted Payment"),
           # count_accts = length(unique(utility_acct_number)) ,
            count_churn = sum(default_tag !=0 & default_tag !="Defaulted Payment")/length(unique(date_concat))) #%>%

## `summarise()` has grouped output by 'user_id'. You can override using the
## `.groups` argument.

 # filter(count_accts > 1) 

temp

## # A tibble: 812 × 6
## # Groups:   user_id [620]
##    user_id utility_acct_number tenure count_accts default count_churn
##      <dbl> <chr>                <int>       <int>   <int>       <dbl>
##  1      17 1769073011              23          23       0        0   
##  2      19 7989248005               3           3       0        1   
##  3      31 689005016               21          44       0        2.10
##  4      32 21002383038             22          23       0        0   
##  5      33 2155441000              15          30       0        2   
##  6      33 2536130080              17          34       0        2   
##  7      37 21003282874             22          46       0        0   
##  8      38 21001139837             22          69       0        0   
##  9      39 7376061001              22          44       0        0   
## 10      42 4381440011              15          15       0        1   
## # … with 802 more rows

Results

Model

A logit model is deployed to analyze the probability of a home churning. The model in brief is described below. Without additional data collected from Experian, limited variability can be measured due to NA values in addition to limited number of coefficients to measure.

In the limited data available, statistically significant effects were measured for probability of churn for both tenure (Months) and days late. Due to relatively small number of observations of late payments, no statistically significant results were measured in probability of late or default payments.

\[\begin{equation} P_{d} = \beta_{0} + \beta_{1}*Months +\beta_{2}*(Payment Method = Card) +\beta_{3}*Income=Low \\ +\beta_{4}*Solar kwH + \beta{5}*(Solar Farm=Howell) \end{equation}\]

## 
## Call:
## glm(formula = Churn ~ tenure + payment_method + Income + temp_solar + 
##     solar_farm, family = binomial(link = "logit"), data = joined)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -2.8845  -0.4531  -0.4198   0.2479   2.2907  
## 
## Coefficients:
##                        Estimate Std. Error z value       Pr(>|z|)    
## (Intercept)             5.26675    1.03903   5.069 0.000000400133 ***
## tenure                 -0.26409    0.04308  -6.131 0.000000000876 ***
## payment_methodcard     -0.24492    0.51325  -0.477          0.633    
## IncomeLow               0.55029    0.63145   0.871          0.383    
## temp_solar             -0.01833    0.04537  -0.404          0.686    
## solar_farmHowell (O&R) -1.15128    0.50626  -2.274          0.023 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 276.31  on 239  degrees of freedom
## Residual deviance: 176.59  on 234  degrees of freedom
##   (572 observations deleted due to missingness)
## AIC: 188.59
## 
## Number of Fisher Scoring iterations: 5

The logit curves below show the relationship between the distribution of both tenure and days late with the probability of churning. The first graph shows that the longer the tenure, the lower the likelihood. The second graph shows that the days of late payments are generally not associated with likelihood of churn.

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